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11 May 2001: 1/2. , so two such numbers must multiply to something of modulus at least 5. ... Analogues of Euclid's algorithm work in other contexts, such as the ring of all polynomials with rational coefficients.

22 Oct 2001: 3. =. (π. p4. )3. 6= 1. Proof. Let B {1, 4, 7} such that{p1p2B 6 1 (mod 9)p3p4B 6 1 (mod 9). ... Take a prime π Z[ω] such that N(π) B (mod 9).

11 Dec 2001: such that V [,] = K(,) : Kop K Cat, e and i form a retractequivalence, and. ... We often write f =(f, f̄) : A B for such a pseudo-map, the 2-cell usually being understood.

24 Nov 2001: 8. A real number is a partition of the rational numbers into two sets A and B such that every element of A is less than every element of B. ... B such that (a,b) is in F.

4 Oct 2001: Of course, we could say something like there exists a constant lambda such that a. ... x[y]-y[x]]. 2. =0. I put the square in because one always likes to expand such an expression in terms of inner products.

13 Dec 2001: Then there is some point c in (a,b) such that f'(c) equals (f(b)-f(a))/(b-a). ... x. 2. <. x. n. =b such that the intervals corresponding to neighbouring x.

7 Nov 2001: Because of irritating difficulties such as the need to carry digits and to identify 0.999999. ... all y(n) such that y is in B.

12 Oct 2001: In each case η is an involution of X1(m), permuting the cusps, such that. ( ... We choose f H2(K,K(T)) such that f and y have the same imagein H2(K,K(T)/K. ).

23 May 2001: then construct a new sequence v in such a way that the first two terms of v mean that it is not a multiple of v. ... If the vector space V is infinite-dimensional, then this means that V contains a subset B such that every vector v in V is a linear